Ray Optics and Optical Instruments Class 12 Notes | CBSE Physics Chapter 9

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Chapter summary

Ray Optics and Optical Instruments (Class 12 Physics) treats light as straight-line rays and explains reflection and refraction at mirrors and lenses. The mirror formula 1/v + 1/u = 1/f and the lens formula 1/v - 1/u = 1/f, with magnification m, locate and size images for spherical mirrors and lenses. Refraction is governed by Snell’s law n1 sin i = n2 sin r, which also gives total internal reflection beyond the critical angle. Lens power P = 1/f (in dioptres) and the lensmaker’s formula let you combine lenses, which is how the human eye, microscope and telescope form magnified images.

Chapter notes

Key Concepts

1. Refraction at Spherical Surfaces

n₁/u + n₂/v = (n₂ − n₁)/R (single refracting surface)

2. Lens Maker’s Formula

1/f = (n − 1)[1/R₁ − 1/R₂]

Thin lens formula: 1/v − 1/u = 1/f

Magnification: m = v/u

Power: P = 1/f (in metres); unit: Dioptre (D)

3. Total Internal Reflection (TIR)

When light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle (ic), all light is reflected back - no refraction.

sin ic = n₂/n₁ (where n₁ > n₂)

Applications: Optical fibres (communication), diamond sparkle, mirages, binoculars (Porro prisms)

4. Refraction Through a Prism

n = sin[(A + δm)/2] / sin(A/2) (at minimum deviation)

where A = angle of prism, δm = minimum deviation angle

At minimum deviation: i = e and r₁ = r₂ = A/2

5. Optical Instruments

InstrumentMagnifying Power
Simple microscopem = 1 + D/f (D = 25 cm)
Compound microscopem = (−L/fo)(1 + D/fe), where L = tube length
Astronomical telescope (normal adjustment)m = −fo/fe; Length = fo + fe

Solved Examples

Example 1

Find the critical angle for glass (n = 1.5) to air.

Answer: sin ic = 1/n = 1/1.5 = 0.667; ic = sin⁻¹(0.667) = 41.8°

Example 2

An astronomical telescope has objective focal length 100 cm and eyepiece focal length 5 cm. Find magnification and tube length in normal adjustment.

Answer: m = fo/fe = 100/5 = 20. Length = fo + fe = 100 + 5 = 105 cm

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Important Questions for Board Exams

3-Mark

  1. Derive the lens maker’s formula.
  2. What is total internal reflection? State conditions and give two applications.
  3. Derive the prism formula for minimum deviation.

5-Mark

  1. Draw a ray diagram of a compound microscope and derive its magnifying power.
  2. Derive the refraction formula at a single spherical surface. Use it to derive the lens maker’s formula.

Quick Revision Points

  • Single surface: n₁/u + n₂/v = (n₂ − n₁)/R
  • Lens maker: 1/f = (n−1)(1/R₁ − 1/R₂); Thin lens: 1/v − 1/u = 1/f
  • TIR: sin ic = n_rarer/n_denser; needs denser→rarer and i > ic
  • Prism: n = sin[(A+δm)/2]/sin(A/2)
  • Telescope: m = fo/fe; length = fo + fe (normal adjustment)
  • Microscope: m ≈ (L/fo)(D/fe) for large magnification

Previous: Ch 8 - EM Waves
Next: Ch 10 - Wave Optics

🃏 Flash Cards: Ray Optics & Optical Instruments

Class 12 Physics · Chapter 9 – swipe through all 8 cards to understand the whole chapter.

🪞Start here1/8

Spherical Mirrors

Mirror formula relates object, image and focal length.

1/v + 1/u = 1/f , f = R/2

Sign convention: distances from pole

  • Concave: real f (converging)
  • Convex: virtual f (diverging)
  • Follow the sign convention
🔎Image size2/8

Magnification (Mirror)

Ratio of image height to object height.

m = − v / u = h’ / h

m < 0 → real, inverted

  • |m| > 1 enlarged
  • |m| < 1 diminished
  • m > 0 → virtual, erect
💧Bending of light3/8

Refraction & Snell’s Law

Light bends when it changes medium; speed changes.

n1 sinθ1 = n2 sinθ2

n = c / v (refractive index)

  • Denser medium: light bends toward normal
  • n has no unit
  • Frequency stays the same
⚪Curved surface4/8

Refraction at a Spherical Surface

Refraction at a single curved boundary between media.

n2/v − n1/u = (n2 − n1)/R

Builds the lens maker’s formula

  • R positive if centre is on outgoing side
  • Used twice for a lens
  • Sign convention applies
🔬Lenses5/8

Lens Maker’s & Lens Formula

Focal length from the lens shape; then image position.

1/f = (n−1)(1/R1 − 1/R2) · 1/v − 1/u = 1/f

Power P = 1/f (dioptre, D)

  • Convex lens: +f
  • Concave lens: −f
  • P in D when f in metres
🪟Trapped light6/8

Total Internal Reflection

Light fully reflects back inside a denser medium.

sin θ_c = 1 / n (θ > θ_c)

Dense → rare, beyond critical angle

  • Optical fibres
  • Mirage & sparkle of diamond
  • Only dense → rarer medium
🔺Dispersion7/8

Prism

A prism deviates and disperses light.

A + δ = i + e · n = sin((A+δ_m)/2) / sin(A/2)

δ_m = minimum deviation

  • δ minimum when i = e
  • Splits white light (dispersion)
  • A = angle of prism
🔭Instruments8/8

Microscope & Telescope

Magnifying power of compound optical instruments.

Microscope M = (L/f0)(D/f_e) · Telescope M = f0/f_e

Objective f0 , eyepiece f_e

  • Microscope: both f small
  • Telescope: f0 large, f_e small
  • D = 25 cm (near point)
Swipe →Click a card to focus →8 cards
📝 Practice Ray Optics and Optical Instruments — 10 NEET PYQs
Real previous-year questions · with answers & solutions
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Q1NEET 2021
Find the value of the angle of emergence from a right-angled prism (refractive index √(3)) when light is incident normally on the vertical face and strikes the hypotenuse, the angle of the prism at the relevant face being 30°.
Correct answer: A. For normal incidence on the first face, r₁=0, so r₂=A=30°. Snell’s law at the second face: √(3)sin 30°=1·sin e, giving sin e=(√(3))/(2), so e=60°.
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Q2NEET 2021
A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror is put perpendicular to the principal axis 40 cm from the lens, the final image is formed at:
Correct answer: D. Lens forms image at (1)/(v)=(1)/(30)-(1)/(60)=(1)/(60), so v=60 cm behind the lens (20 cm behind the mirror). The mirror reflects this to a real image 20 cm in front of it; this then re-images through the lens. By symmetry the final image coincides with the object and is virtual, 20 cm from the plane mirror.
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Q3NEET 2021
A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept along the same axis with a distance d between them. A parallel beam falling on A leaves B as a parallel beam. Then the distance d (in cm) is:
Correct answer: B. The parallel beam converges to the focus of A (20 cm beyond A). For B to re-collimate it, this point must be at the focus of the concave lens, i.e. 5 cm before B. So d=20-5=15 cm.
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Q4NEET 2020
An object is placed on the principal axis of a concave mirror at a distance of 1.5f (f is the focal length). The image will be at:
Correct answer: A. Mirror formula (1)/(v)+(1)/(u)=(1)/(f) with u=-1.5f and f=-f: (1)/(v)=-(1)/(f)+(1)/(1.5f)=(1)/(f)(-1+(2)/(3))=-(1)/(3f), so v=-3f (real, in front of the mirror).
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Q5NEET 2020
If the critical angle for total internal reflection from a medium to vacuum is 45°, then the velocity of light in the medium is:
Correct answer: B. μ=(1)/(sin i_c)=(1)/(sin45°)=√(2). Since μ=(c)/(v), v=(c)/(√(2))=(3×10⁸)/(√(2))=(3)/(√(2))×10⁸ m/s.
🔎 See the full step-by-step solution in the app →
Q6NEET 2020
The power of a biconvex lens is 10 D and the radius of curvature of each surface is 10 cm. The refractive index of the material of the lens is:
Correct answer: D. f=(1)/(P)=(1)/(10) m =10 cm. Lens-maker: (1)/(f)=(μ-1)((1)/(R₁)-(1)/(R₂))=(μ-1)((1)/(10)+(1)/(10)). So (1)/(10)=(μ-1)(2)/(10), giving μ-1=(1)/(2), μ=(3)/(2).
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Q7NEET 2018
An object is placed 40 cm from a concave mirror of focal length 15 cm. If the object is moved 20 cm towards the mirror, the displacement of the image will be:
Correct answer: B. u₁=-40,f=-15: (1)/(v₁)=(1)/(f)-(1)/(u₁)=-(1)/(15)+(1)/(40) gives v₁=-24 cm. After moving, u₂=-20: (1)/(v₂)=-(1)/(15)+(1)/(20) gives v₂=-60 cm. Image shifts from 24 cm to 60 cm in front, i.e. 36 cm away from the mirror.
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Q8NEET 2017
A thin prism having refracting angle 10° is made of glass of refractive index 1.42. It is combined with another thin prism of glass of refractive index 1.7 to produce dispersion without deviation. The refracting angle of the second prism should be:
Correct answer: B. Net deviation zero: (μ₁-1)A₁=(μ₂-1)A₂, so A₂=(μ₁-1)/(μ₂-1)A₁=(0.42)/(0.7)×10°=6°.
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Q9NEET 2016
An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance:
Correct answer: C. Objective: u=-200,f=40: (1)/(v)=(1)/(40)-(1)/(200)=(4)/(200)=(1)/(50), so v=50 cm. The eyepiece forms the final image at infinity (normal adjustment), so separation =v+fₑ=50+4=54 cm.
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Q10NEET 1996
A convex lens of focal length 80 cm and a concave lens of focal length 50 cm are combined in contact. Their resulting power is:
Correct answer: D. P=(100)/(f₁)+(100)/(f₂)=(100)/(80)+(100)/(-50)=1.25-2.0=-0.75 D.
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Frequently Asked Questions

What is the difference between a real and a virtual image in ray optics?

A real image forms where light rays actually meet and can be caught on a screen; it is inverted. A virtual image forms where rays only appear to meet, cannot be caught on a screen, and is erect. A concave mirror or convex lens can form both, while a convex mirror or concave lens always forms a virtual, erect image.

What are the mirror and lens formulas in Class 12 ray optics?

The mirror formula is 1/v + 1/u = 1/f and the lens formula is 1/v - 1/u = 1/f, where u is the object distance, v the image distance and f the focal length, using the sign convention. Magnification m = -v/u for mirrors and m = v/u for lenses.

What is total internal reflection and when does it occur?

Total internal reflection happens when light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle, so all the light reflects back instead of refracting. It is why optical fibres and diamonds work and is governed by Snell’s law.

What is the power of a lens and its unit?

The power of a lens is P = 1/f, the reciprocal of its focal length in metres, and its unit is the dioptre (D). A converging (convex) lens has positive power and a diverging (concave) lens has negative power; when lenses are combined, their powers add.

Why is the ray optics chapter important for NEET and board exams?

Ray optics is high-yield: it carries direct numerical questions on mirrors, lenses, refraction and optical instruments in both the CBSE board exam and NEET. Mastering the sign convention and the mirror and lens formulas reliably earns those marks.

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